Vickrey Bidding Strategy

Here’s the e-mail from Mikkel concerning Vickrey bidding strategy.  I’m including my answer, but really want as many listeners as possible to weigh in.  Either post your responses as a comment to this blog entry or e-mail us at baseballchannel@mlb.com.  Your thoughts will be shared on Monday’s 411!

Hi again!

Refining my argument:

First of all, when bidding for free agents, yes, you are looking at true value: True value means ALL things considered – that is, also scarcity, needs, and everything. It doesn’t mean draft day value.

Okay, you bid $14 for a $10 player. Three things can happen:

1) The next-highest bid is higher than $10: I already discussed this in the previous mail. Conclusion: not good.
2) The next-highest bid is lower than $10: You get the player at a discount, but you would have anyway if you had bid $10.
3) The next-highest bid is exactly $10: You either get the player or you don’t, depending on the rules of the league. But it still wouldn’t have been a better idea for you to bid, for example, $11, because then you would lose on the acquisition of the player (since you estimate his value to be $10).

If you’re still not convinced (and it doesn’t sound like it), can you please open a blog post so it can be discussed in detail?  Thanks guys!

Mikkel from Denmark

I’m not convinced, Mikkel!  Here’s why.  I think you’re underestimating the power of competition.  Even if you estimate a player’s    “true value” to be $10, there’s a good chance you’ll bid a few dollars higher due to the fact that you really want the player.  At that moment, you’re looking to make your team better.  It’s not going to matter if you pay $14 or even $20.  All that matters is whether you give yourself the best possible chance of obtaining him (and keeping him away from your competitors) without ridiculously overspending.  And what is “true value” anyway?  How do you calculate it?  Doesn’t “true value” depend as much on the other league owners’ evaluation of the player as on your own?  These are the factors which lead me to prefer a fairly aggressive approach when it comes to Vickrey bidding.

Zach Steinhorn, MLB.com      

9 Comments

I’ll try to clarify what I mean by “true value”.

By a player’s Estimated True Value (let’s call it ETV) I mean YOUR estimate of the amount of FAAB money or auction dollars that a given player’s production will be worth ALL THINGS CONSIDERED. This includes the following considerations:

1) Your estimate of the player’s mean production from this point of the season and out (“mean” in the probability theory sense).

2) Your place in the standings in each individual category, and whether you can close any gaps by acquiring the player.

3) The other owners’ places in the standings (i.e. can you hurt a rival by getting the player).

4) Whether it is a keeper league or not.

5) Scarcity – both position scarcity and player pool scarcity.

6) Your amount of remaining FAAB money or auction dollars (e.g. do you wish to use a large chunk of your cash to secure one player or would you rather shoot for two smaller fish).

7) Your personal risk profile, i.e. whether you like gambling on the young studs or prefer the more reliable old workhorses.

8) Etc.

Now, how do you put dollar prices on all these factors you ask? Well, that’s every fantasy player’s real challenge. You can use gut instincts, PECOTA forecasts or similar systems, or just ask Mike and Cory (but be sure to include a Lebowski quote). But it isn’t different from what, for example, a stock broker needs to do when deciding to invest in certain companies. You need to make a qualified estimate ALL THINGS CONSIDERED.

When you have “calculated” a player’s ETV like this, you do not want to acquire him for any more than that value, because – according to your estimate – you will lose on him ON AVERAGE. Maybe he’ll get ridiculously hot or maybe he’ll go stone cold. But on average you have estimated that he will not be worth the investment. In this sense, the ETV does not depend on the other league’s evalution of the player (although the player pool scarcity is affected by it, of course).

I do realize that there are certain qualifications that need to be done. First, you may not be very rational about a player (e.g. if you think his name sounds funny). Second, you may just want to thwart the plans of a certain league rival and don’t care about your own fate. But this is where mathematics and game theory stop and irrationality enters the picture. My argument is only based on a league where everyone wants to maximize their profits, i.e. place in the standings, and all your (Mike’s, Cory’s and Zach’s) counter arguments have been based on the same foundation.

Therefore, Vickrey bidding should NEVER encourage a rational bidder to bid above (or below) one’s ETV of a player. If you bid $70 dollars and get the player for $10, chances are you’re either really optimistic about the player or that you have failed in the strategic part of the game.

This does not apply to a regular auction. If you know with a given certainty that the other bidders are going to bid $8 for a player that you think is worth $10, it might be wise to bid $9 in a regular draft. But as I’ve tried to explain, Vickrey erases this kind of speculative bidding.

Man, this is a long post.

Sincerely,

Mikkel from Denmark

“Therefore, Vickrey bidding should NEVER encourage a rational bidder to bid above (or below) one’s ETV of a player. If you bid $70 dollars and get the player for $10, chances are you’re either really optimistic about the player or that you have failed in the strategic part of the game.”

I disagree totally with his statement. If everyone else is “rational” you would certainly want to overbid.

My point, however, is to call for the elimination of vickery bidding altogether.

I think that statement from Mikkel points to the fallacy of Vickrey bidding. If every other player were “rational”, clearly the correct strategy would be to bid all your money on any player you wanted. You would get every player and only pay $1 more than their true value.

So, the real question for me is why would a league ever use this method? At best, in a “rational” league, it rewards owners who are incapable of assessing a player’s true value or those who are taking advantage of everyone else’s rational nature. They may bid $100 for Joba Chamberlain, but only have to pay $21. At it’s worst, in an “irrational” league in which several players employed an over-dependence upon this bidding, it seems that it would create havoc if you really did pay $100 for Joba.

It seems to me that the logical equivalent of Vickery bidding would be to reward GMs who make bad trades. If you give up Pujols for Lincecum and Melky Cabrera, you would have the trade nullified and you would only have to give up someone equal to the next best offer for Lincecum and Melky.

Traditional FAAB, where each player bids what the player’s worth is to him (I’m glad to see Mikkel cleared up the definition of “value”) knowing for certain he will have to pay that amount is clearly the better method of bidding.

Vickery rewards owners who are uninformed. To me, that’s enough of a reason to avoid it.

I’m sorry, but that is just plain wrong. As I argue in my e-mail, a rational player should never bid more than the ETV for a player. This can be proved rigorously using mathematical methods, or you can just look at it in plain words (as I did above).

By definition, the ETV of a player is the most you want to bid for him. If you get him for more than that, it represents a net loss (on average, according to your estimate). Therefore, if you in a Vickrey auction bid all your money on a player you want (as the previous blog poster suggested), you are running the risk that the next-highest bid is larger than your ETV, so you get to pay more for the player than his ETV, which – again, by definition – is a bad thing (on average and according to your estimate). If the next-highest bid isn’t larger than your ETV, well, that’s just gravy. But in this case you would still have gotten the player if you had chosen the less risky optimal strategy: Simply bidding the ETV.

To sum it up: In a Vickrey auction, all rational players will bid exactly their individual ETV’s of the player in question. This doesn’t mean that the bids will be equal, of course, because different owners have different evalutions. But it erases the speculative bids that you sometimes encounter in regular auctions.

For more on the math behind Vickrey auctions, check out the book “Intermediate Microeconomics” by Hal R. Varian, ch. 17 (7th edition).

I have to admit that I got the argument in my e-mail a bit wrong under no. 3.

If you bid $14 and the next-highest bid is $10 (= your ETV), obviously you are certain to get the player, but for $11 which is a net loss for you and therefore bad. If you in this case had bid your ETV, the league’s tiebreaker rules would decide which of you get the player for $11, so there would only be a certain CHANCE that you lose on the deal.

So the conclusion is the same: You should always bid the ETV.

By the way, there’s (naturally) a Wikipedia article about Vickrey auctions:

http://en.wikipedia.org/wiki/Vickrey_auction

It doesn’t explain the logic but does state the conclusion that I have derived here. Note that in the “Weaknesses” paragraph, none of the drawbacks of the Vickrey auction really apply to fantasy baseball, since there’s no “seller” in free agent auctions.

Actually, if you see it as an objective to make other owners spend as much of their FAAB as possible, sometimes bidding above your ETV can be a viable strategy in Vickrey.

For instance, suppose you’re bidding on a player whose ETV is $10. You have a strong suspicion that another team values the player more highly at, say, $15. In this case it might be smart of you to bid $14 to milk FAAB from your rival. However, you have to be REALLY certain that your rival’s ETV is indeed $15 or higher, because if it’s lower than $14 you will suffer a substantial net loss as described in earlier posts.

Also, in most cases, other owners will have about the same ETV as the highest bidder, so quite often the auction winner will get to pay a price which isn’t that far from his own bid – even in Vickrey. Therefore, this FAAB milking strategy is generally not very effective and pretty risky.

Note also, that it is still NEVER smart to bid more than your ETV if your plan is to actually acquire the player – only if you wish to mess with the winning owners’ FAAB.

guys
i never been an auction league(but looking for one), but one thing i do know with salary or draft position, during the season, values are fluid and never stationery. The salaries and positions change based on not only value of said player, but also contigent on values of other playes not changing.

chris from williamsport

Maybe it’s just the Tell-Tale voices in my head (just kidding, Mike), but I feel obligated to respond to the inaccuracies uttered on today’s show. This is not an attempt to put anybody down, just an attempt to get the truth out in a good spirit. :)

I must say that I’m a bit disappointed that nobody seems to read my entire argument. I know it’s long but so far everybody has missed my key points.

1) Pete in Jordan said that I don’t understand the difference between free agent bidding and draft day auctions. This claim can’t be based on anything I have written, because all my rants deal with free agent auctions alone (although the concept of “true value” applies to draft day auctions as well).

2) Mike says that it doesn’t matter whether you bid $15 for a $10 player, because you’re just happy that you get the player and that he can help your team. Well, if this is true, then what Mike calls the player’s value isn’t his ETV, because the ETV should take into account whether you are desperate for the player’s production and your risk profile. By definition, “overbidding” is bad for you.

3) Cory says that I forget the opportunity cost of not getting the player. This is wrong as the opportunity cost is covered by the points 1 and 5 in my post about “calculating” ETV. If it would hurt you badly if you don’t get the player – either because of his expected production or because of player pool scarcity – then the ETV should reflect that.

4) Cory and Mike claim that irrationality plays a large part in fantasy baseball. This I can agree with. However, that doesn’t change the conclusion on Vickrey bidding. Injuries, for instance, isn’t an “irrationality” at all – it affects player pool scarcity and therefore the ETV. Another owner’s sick mom is an irrationality, but why would that make you bid more than your ETV? My arguments are indeed based on a rational framework, but adding irrationality doesn’t change the logic. First of all because your ETV (and therefore your bidding strategy) almost doesn’t depend on the other owners’ actions, and secondly because irrationality by definition isn’t measurable and therefore can be disregarded. If it WAS measurable then it would be something that everybody could account for in their respective ETV’s.

5) Cory agrees with the argument of David the blog poster. As I show above, this is erroneous. If you know that a certain player has adopted the strategy of always bidding his entire FAAB on a player he wants, then I encourage you to look up his remaining FAAB and bid that amount minus $1. This way, your foolish rival will only have $1 left in his FAAB deposit after the first free agent auction of the season. Clearly, this can’t be called the optimal strategy.

6) Cory says that my stock broker analogy doesn’t apply to fantasy baseball at all. It is true that there are clear differences (for example the scarcity part which Cory mentions) but that doesn’t make the analogy any less meaningful. The important thing is that the stock broker has to take many different aspects other than the share’s market value in itself into account when determining its “true value”. If you don’t like the analogy, here’s another one: You go to the marketplace to buy fruit for a fruit salad. You only have a certain amount of money and you know that your parents-in-law will be expecting a grand meal. There is only a very limited amount of fruit available in the market, and there are other buyers as well. Here you have to take adjust for everything (the deliciousness of the fruit, the scarcity, and even the cost of returning home without having bought anything) when determining “true value”.

I hate that I’m beginning to look obsessed and stubborn, but most of these points stem from the fact that nobody takes it seriously when I write “all things considered”. It is true that the ETV is influenced by a huge number of things – and that the ETV can change rapidly – but it is downright silly to just treat what Mike and Cory call “irrationalities” as intangibles which shouldn’t be accounted for. When you adjust for those there is only one optimal strategy: bidding the ETV.

Again: I’m not angry at anybody and I’m quite happy that we’re discussing this! I just feel it is unfair to not take my arguments literally. Please let me know if you need to get some things cleared out.

Mikkel from Denmark

hey everyone longtime listener firsttime…poster?

Mikkel, well done explaining the logic of Vickrey (and big ups for invoking Varian, the king of all econ texts!). The big thing that makes Vickrey different is of course that the price you bid doesn’t determine the selling price. In a normal auction, the winner’s bid determines the price; in Vickrey, the first loser’s bid sets the price. In this way the winner has no way to control the sale price.

I personally don’t think Vickrey is the best choice for fantasy baseball because it takes the gambling out of the system, and I like the extra chance to create a game where the amount you bid can be a risk. Vickrey, on the other hand, takes away the opportunity to get a big steal in the FAAB market.

Rory in Vancouver

First of all, I love the show. You guys have made me a better FBB manager.

I think a main point of confusion in this discussion is in the concept of valuation. Mike & Cory seem to be talking about valuation as if there is a single true value for a player. However, we could instead think of each bidder as having their own valuation for a player. I think this latter approach (which happens to be the standard approach economists use in thinking about auctions), will resolve some of the issues of disagreement.

When Mike & Cory say that they are willing to overpay for a player, what they really mean (i think) is that they have a high valuation for that player, that is they have a high willingness to pay. What a vickrey auction does is make it a dominant strategy to always report your true willingness to pay. One bidder’s willingness to pay may be higher or lower than another’s (due to fund constraints, position constrainsts, and all of the other factors Mikkel and others have mentioned) and still be completely rational.

It is clear that if the most you would be willing to pay for a given player is $25, then bidding $100 for a player is not a good idea, because someone else may value that player at $75, and you would be stuck paying $51 more than you were willing to pay. Instead, you should always bid $25 for that player, whether you think the other players are bidding rationally or not. Bidding $25 is the only way to both ensure that you don’t overpay, and that you won’t miss out on an opportunity to get the player for less than your personal valuation. If you say that you should bid more, and would be happy to get the player for, say, $30, then what you really are saying is that your true willingness to pay is above $25.

What a vickrey auction does NOT do, is extract the true market valuation of a player. Actually this concept is not even well-defined, as the market mechanisms employed are important to the actual price that is paid. In a situation where every bidder has a different valuation of a player, there is no single “market value” that is independent of the mechanism used to allocate the prize. All the Vickrey auction does is (given rational bidders) allocate the prize to the bidder with the highest willingness to pay.

If bidders are not rational, then the vickrey auction will penalize irrational bidders, since they will sometimes win the prize and pay more than they were willing to pay (because their bid was too high), or they will lose the prize when they could have won it for less than they were willing to pay (because they bid too low).

Again, I think the main confusion in this discussion is in assuming there is a single “market value”. This is simply not the case. we all know that a team that needs saves will be willing to pay a lot more for a free agent closer, than a team that already has k-rod, nathan, and coco. The mechanism for allocating the player to a team, be it a vickrey auction, or simply waiver priority, will determine the price paid and who receives the prize. The Vickrey auction happens to have the nice property that (under rationality) the player with the highest willingness to pay will win.

Thanks to Mikkel for putting his thoughts out there. I think that mostly he gets it right. Hope this helps.

Elias in Ann Arbor

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